There is a pressing need to understand how different delta morphologies arise because morphology determines a delta's ecologic structure, resilience to relative sea-level rise, and stratigraphic architecture. We use numerical modeling (Delft3D) to explain how deltaic processes and morphology are controlled by the incoming sediment properties. We conducted 36 experiments of river-dominated delta formation varying the following sediment properties of the incoming grain-size distribution: the median, standard deviation, skewness, and percent cohesive sediment, which is a function of the first three properties. Changing standard deviation and skewness produces minimal morphological variation, whereas an increase in dominant grain size (D84) and decrease in percent cohesive sediment produce a transition from elongate deltas with few channels to semicircular deltas with many channels. This transition occurs because critical shear stresses for erosion and settling velocities of grains set the number of channel mouths and the dominant delta-building process. Together, the number of channel mouths and the dominant process—channel avulsion, mouth bar growth, or levee growth—set the delta morphology. Coarse-grained, noncohesive deltas have many channels dominated by avulsion, creating semicircular planforms with relatively smooth delta fronts. Intermediate-grained deltas have many channels dominated by mouth bar growth, creating semicircular planforms with rugose delta fronts. Fine-grained, cohesive deltas have a few channels, the majority of which are dominated by levee growth, creating elongate planforms with smooth delta fronts. The process-based model presented here provides a previously lacking mechanistic understanding of the effects of sediment properties on delta channel network and planform morphology.